JPS63302317A - Positional speed measuring apparatus of moving object - Google Patents

Positional speed measuring apparatus of moving object

Info

Publication number
JPS63302317A
JPS63302317A JP13827587A JP13827587A JPS63302317A JP S63302317 A JPS63302317 A JP S63302317A JP 13827587 A JP13827587 A JP 13827587A JP 13827587 A JP13827587 A JP 13827587A JP S63302317 A JPS63302317 A JP S63302317A
Authority
JP
Japan
Prior art keywords
error
speed
kalman filter
output
reference device
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP13827587A
Other languages
Japanese (ja)
Inventor
Tomohisa Konishi
小西 朝久
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Mitsubishi Heavy Industries Ltd
Original Assignee
Mitsubishi Heavy Industries Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Mitsubishi Heavy Industries Ltd filed Critical Mitsubishi Heavy Industries Ltd
Priority to JP13827587A priority Critical patent/JPS63302317A/en
Publication of JPS63302317A publication Critical patent/JPS63302317A/en
Pending legal-status Critical Current

Links

Abstract

PURPOSE:To enable accurate correction of errors of a global position measuring system (GPS) receiver output, by correcting an output of an inertia reference device by an error vector calculated with a Kalman filter. CONSTITUTION:An inertia reference device 1 is equipped with a gyroscope, a sensor block having an accelerometer and a computer section and outputs signals pertaining to the position, speed and attitude of an airplane. Position and speed signals of the device 1 and a GPS receiver 2 are inputted into a Kalman filter 3. An error correction calculating section 2a calculates an error correction value used as value indicating the degree of a degrading in a position error of the GPS receiver 2 based on a relative relationship between positions of an airplane and a satellite. Then, the Kalman filter 3 generates an error vector based on outputs from the GPS receiver 2 and the error correcting section 2a. Then, a correction section 1a inputs the error vector into a direction cosine matrix updating device, a position calculator and a speed calculator to perform calculations and outputs signals of attitude angle, position and speed with limited errors.

Description

【発明の詳細な説明】 〔産業上の利用分野〕 本発明は、航空機、船舶、ロケット、自動車等の移動体
に搭載される位は速度の測定装置に関する。
DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a speed measuring device mounted on a moving object such as an aircraft, a ship, a rocket, or an automobile.

〔従来の技術〕[Conventional technology]

従来、移動体の位置、速度、姿勢角を測定する装置とし
ては、慣性基準装置がよく用いられている。しかし、慣
性基準装置が出力する位置、速度、姿勢角には誤差が含
まれており、特に位置誤差は装置の作動時間の経過につ
れて増大していく。そこで、慣性基準装置の出力に含ま
れる誤差を軽減し、長時間精度の良い位置速度測定装置
とすることを目的として、慣性基準装置と他の位置速髪
測定装fit()”ツプラ航法装置や全地球測位システ
ム(GxobalPositioning Syste
m (本明細書では以下これをGPSと呼ぶことにする
)受信機など)を組合せることが考案されている。
2. Description of the Related Art Conventionally, an inertial reference device is often used as a device for measuring the position, speed, and attitude angle of a moving body. However, the position, velocity, and attitude angle output by the inertial reference device include errors, and in particular, the position error increases as the device operates. Therefore, with the aim of reducing the error included in the output of the inertial reference device and making it a position and speed measuring device with good long-term accuracy, we have developed an inertial reference device and other position and speed measuring devices such as ``fit()'' Tsupura navigation device and Global Positioning System
m (hereinafter referred to as GPS) receiver, etc.).

この場合、第6図に示すように、位置誤差、速度誤差な
どを要素とする誤差ベクトルをカルマンフィルタ計算に
より推定し、これによって誤差を補正する方法がよく用
いられている。このカルマンフィルタでは、慣性基準装
置が出力する位置、速度信号と他の位置、速度測定装置
が出力する位置、速度信号との差を観測ベクトルとして
入力しこれに基づいて誤差ベクトルを出力するようにな
っている。
In this case, as shown in FIG. 6, a method is often used in which an error vector including position error, velocity error, etc. is estimated by Kalman filter calculation, and the error is corrected using this estimation. In this Kalman filter, the difference between the position and speed signal output by the inertial reference device and other positions, the position and speed signal output by the speed measuring device is input as an observation vector, and an error vector is output based on this. ing.

上記他の位置速度測定装置が出力する位置、速度信号に
は誤差が含まれており、これが観測ベクトルの誤差とな
るために、通常この誤差をカルマンフィルタに観測雑音
として盛込むことが行われており、この観測雑音の値と
しては誤差の平均的な値力≦用いられている。
The position and speed signals output by the other position and speed measuring devices mentioned above contain errors, and since these become errors in the observation vector, this error is usually incorporated into the Kalman filter as observation noise. , the average value of the error is used as the value of this observation noise.

〔発明が解決しようとする問題点〕[Problem that the invention seeks to solve]

慣性基準装置と組合せる他の位置速度測定装置としてG
PS受信機を用い、第6図に示すような方法で誤差を補
正する場合、GPS受信機が出力する位置、速度の誤差
は、GPS受信機の地球上での位置とGPS受信機がそ
の電波を受信しているGPS用の衛星の位置との相対的
な位置関係に応じて変化する。
G as another position and velocity measuring device in combination with an inertial reference device
When using a PS receiver and correcting the error using the method shown in Figure 6, the error in the position and speed output by the GPS receiver is determined by the position on the earth of the GPS receiver and the radio wave detected by the GPS receiver. It changes depending on the relative positional relationship with the position of the GPS satellite receiving the signal.

この相対的な位置関係は、GPS受信機を搭載した移動
体の移動及びGPS用の衛星の移動によって、時々刻々
変化する。したがって、カルマン・フィルタに盛込まれ
た観測雑音の値が平均的な値では、実際の観測ベクトル
に含まれる観測誤差がカルマンフィルタに盛込まれた観
測雑音と合わなくなることがあり、推定する誤差ベクト
ルの精度 。
This relative positional relationship changes from time to time due to the movement of the mobile body equipped with the GPS receiver and the movement of the GPS satellite. Therefore, if the value of the observation noise included in the Kalman filter is an average value, the observation error included in the actual observation vector may not match the observation noise included in the Kalman filter, and the estimated error vector accuracy.

が劣化することがある。これは結果的に慣性基準装置の
誤差を補正する精度を劣化させることとなり、組合せた
装置としての性能の低下を招く。
may deteriorate. This results in a deterioration in the accuracy of correcting errors in the inertial reference device, leading to a decrease in the performance of the combined device.

本発明は、このような従来のもの〜欠点を解消しようと
するものである。
The present invention aims to eliminate these conventional drawbacks.

〔問題点を解決するための手段〕[Means for solving problems]

この問題を解決するために、本発明では、移動体の位置
、速度信号を出力する、慣性基準装置、衛星から送信さ
れる電波を捕捉し移動体の位置、速度信号を出力するG
PS=i信機、上記慣性基準装置とGPS受信機との出
力を受は両出力の差である観測はクトルに基づいて慣性
基準装置の出力を補正する誤差ベクトルを出力するカル
マンフィルタ及び上記カルマンフィルタにGPS受信機
で検知された移動体の位置と衛星の位置との相対関係に
応じた観測雑音の誤差修正出力を出力する手段とを設け
た。
In order to solve this problem, the present invention uses an inertial reference device that outputs position and speed signals of a moving object, and a G-G system that captures radio waves transmitted from a satellite and outputs position and speed signals of a moving object.
PS=i transmitter receives the output of the inertial reference device and the GPS receiver, and the difference between the two outputs is observed.The observation is performed by a Kalman filter that outputs an error vector that corrects the output of the inertial reference device based on the vector, and the Kalman filter described above. Means for outputting an error correction output of observation noise according to the relative relationship between the position of the moving body detected by the GPS receiver and the position of the satellite is provided.

〔作用〕[Effect]

慣性基準装置からの出力を補正する誤差はクトルは、慣
性基準装置の出力とGPS受信機の出力の差である観測
ベクトルに基づいてカルマン・フィルタ計算によって出
力されるが、更にこのカルマン・フィルタに盛込まれた
観測雑音はGPS受信機で検知された移動体と衛星との
位置との相対的位置関係に応じた誤差修正出力によって
修正される。
The error that corrects the output from the inertial reference device is output by a Kalman filter calculation based on the observation vector, which is the difference between the output of the inertial reference device and the output of the GPS receiver. The included observation noise is corrected by an error correction output according to the relative positional relationship between the moving object and the satellite detected by the GPS receiver.

従って、GPS受信機が出力する位置・速度信号の誤差
は移動体の位置に応じて正確に修正される。
Therefore, errors in the position/velocity signals output by the GPS receiver are accurately corrected according to the position of the moving object.

このように実際に合った観測誤差を表わす誤差修正出力
を用いて正確に観測雑音を修正することによって、慣性
基準装置が出力する位置、速度に含まれる誤差を精度が
劣化することなく補正することが可能である。
In this way, by accurately correcting observation noise using the error correction output representing the actual observation error, it is possible to correct errors included in the position and velocity output by the inertial reference device without deteriorating accuracy. is possible.

〔実施例〕〔Example〕

航空機に適用された本発明の一実施例を第1図〜第4図
によって説明する。第2図に示すように、慣性基準装置
1は、ジャイロ、加速度計を備えたセンサブロック11
と計算機部12を備えていて、ジャイロ、加速度計の検
出値に基づいて航空機の位置n、速度n及び姿勢角21
についての信号を出力する。
An embodiment of the present invention applied to an aircraft will be described with reference to FIGS. 1 to 4. As shown in FIG. 2, the inertial reference device 1 includes a sensor block 11 equipped with a gyro and an accelerometer.
and a computer section 12, which calculates the position n, speed n, and attitude angle 21 of the aircraft based on the detected values of the gyro and accelerometer.
Outputs a signal about .

第3図に示すように、GPS受信機は航空機Pに搭載さ
れていて、4コの衛星A、 B、 C,D、  ・・・
・から送信される電波を受信する。衛星からの電波は、
時刻、衛星位置等のデータを含んでいて、GP8受信機
はこれを捕捉して航空機の3次元位置が測定され位置及
び速度信号が出力される。
As shown in Figure 3, a GPS receiver is installed on an aircraft P, and four satellites A, B, C, D,...
・Receive radio waves sent from. The radio waves from the satellite are
It contains data such as time and satellite position, and the GP8 receiver captures this data to measure the three-dimensional position of the aircraft and output position and speed signals.

第1図に示すように、慣性基準装置1及びGPS受信機
2の位置・速度信号がカルマンフィルタ3ニ入力され、
カルマンフィルタではこの両信号の差であるH 1ff
l+ベクトルを計算し、これに基づいて誤差ベクトルを
出力する。
As shown in FIG. 1, the position and velocity signals of the inertial reference device 1 and the GPS receiver 2 are input to a Kalman filter 3,
In the Kalman filter, the difference between these two signals, H 1ff
The l+vector is calculated and an error vector is output based on this.

更に本実施例においては、誤差修正計算部2aがGPS
受信機2に設けられる。同計算部2aにおいては、例え
ば航空機の位置と衛星の位置との相対関係によるGPS
受信機の位置誤差の劣化の度合いを表わす値として用い
られる誤差修正(PDOP;  Po5ition D
ilution of Precision)を計算す
る機能等航空機の位置と衛星との位置の相対関係によっ
て生ずるGPS受信機の観測誤差を計算する機能を有し
ている。即ち、第4図に示すように、GPS受信機で検
出した時刻及び自機の位置(緯度、経度) 2a−1,
2a−2を入力して、4個の衛星A、B、C,D を還
択してそれらの視線(Line  of Sight、
  LO8)−?クトル(BA 、+23.、(B。。
Furthermore, in this embodiment, the error correction calculation section 2a uses GPS.
It is provided in the receiver 2. In the calculation unit 2a, for example, GPS data based on the relative relationship between the position of the aircraft and the position of the satellite is calculated.
Error correction (PDOP; Po5ition D) is used as a value representing the degree of deterioration of the receiver position error.
It has a function to calculate the observation error of the GPS receiver caused by the relative relationship between the position of the aircraft and the position of the satellite. That is, as shown in FIG. 4, the time and position (latitude, longitude) of the own aircraft detected by the GPS receiver 2a-1,
2a-2, select the four satellites A, B, C, D and set their Line of Sight.
LO8)-? (BA, +23., (B..

■、を得る。次に、これら視線ベクトルの転置行列(a
、T を行列の要素としたIHとその転置行列出7との
積の逆行列により、配置にともなう誤差であるGPS誤
差共分散6を求めるっ誤差修正は、このGPS誤差共分
散Gの対角成分を二乗和したものの平方根として求めら
れる7 この誤差修正が、第1図の誤差修正部2aからの出力と
してカルマンフィルタ3に入力され誤差ベクトルの生成
を行う。ここでカルマンフィルタ3は、第5図のフロー
チャートに従って、時々開側誤差修正PDOP  を入
力しつつカルマンゲインIKn及び観測雑音IRnを演
算し、慣性基準装置t1とGPS受信機2とから構成さ
れる装置の差及び速度の差からなる観測ベクトル、zn
を入力して前記のカルマンゲインIKnとから誤差ベク
トル9n(+1を演算し、これを第1図の慣性基準装[
11の補正部1aに時々刻々出力する。
■, get. Next, the transposed matrix (a
, the GPS error covariance 6, which is the error due to the placement, is calculated by the inverse matrix of the product of IH and its transposed matrix E7, with T as matrix elements.Error correction is performed using the diagonal of this GPS error covariance G. This error correction is obtained as the square root of the sum of the squares of the components.This error correction is input to the Kalman filter 3 as an output from the error correction section 2a in FIG. 1, and an error vector is generated. Here, the Kalman filter 3 calculates the Kalman gain IKn and the observation noise IRn while occasionally inputting the open side error correction PDOP according to the flowchart in FIG. Observation vector consisting of difference and speed difference, zn
is input, an error vector 9n (+1) is calculated from the above-mentioned Kalman gain IKn, and this is converted to the inertial reference device [
It is outputted every moment to the correction section 1a of No. 11.

この補正部1aは第2図に示すように前記の誤差ベクト
ル(姿勢角、位置、速度)を、それぞれ方向余弦行列更
新器1位置計算器及び速度計算器に入力して計算を行い
、誤差の少ない姿勢角21、位1f22、速度n信号を
出力する。
As shown in FIG. 2, this correction unit 1a inputs the above-mentioned error vectors (attitude angle, position, velocity) into the direction cosine matrix updater 1 position calculator and velocity calculator to calculate the error. It outputs small attitude angle 21, position 1f22, and velocity n signals.

本実施例は以上のように構成されているので。This embodiment is configured as described above.

航空機と衛星との相対的位置関係に応じた誤差修正信号
によってカルマンフィルタ3においてGPS受信機出力
と慣性基準装置出力の差である観測ベクトルを入力し、
修正された観測雑音に基づいて誤差ベクトルが出力され
て慣性基準装置の出力が補正されることになる。
An observation vector that is the difference between the GPS receiver output and the inertial reference device output is input to the Kalman filter 3 by an error correction signal according to the relative positional relationship between the aircraft and the satellite,
An error vector will be output based on the corrected observation noise to correct the output of the inertial reference device.

従って、カルマンフィルタには航空機の位置と衛星位置
の相対関係に応じ常に実際に合った誤差修正信号が入力
されて観測雑音が修正され、その修正された観測雑音に
基いて誤差ベクトルが補正されること〜なるので、精度
面で常時安定した性能をもつ位置速度測定装置を実現す
ることができる。
Therefore, an error correction signal that actually matches the relative relationship between the aircraft position and the satellite position is always input to the Kalman filter, the observation noise is corrected, and the error vector is corrected based on the corrected observation noise. . . . Therefore, it is possible to realize a position and velocity measuring device that always has stable performance in terms of accuracy.

〔発明の効果〕〔Effect of the invention〕

以上実施例について具体的に説明したように、本発明は
次の効果を挙げることができる。
As described above in detail with respect to the embodiments, the present invention can bring about the following effects.

即ち、GPS受信機出力と慣性基準装置の出力との差で
ある観測ベクトルをもとに、カルマンフィルタにおいて
林動体の位置と衛星の位置の相対関係に応じた誤差修正
信号によって修正された観測雑音に基づいて計算された
誤差ベクトルによって慣性基準装置の出力が補正される
こと〜なるので、航空機と衛星との相対的位置関係によ
って時々刻々変化するGPS受信機出力の誤差を正確に
修正することができ、従って、位置速度測定装置の精度
を上げ、かつこれを常時安定させることができる。
That is, based on the observation vector that is the difference between the GPS receiver output and the inertial reference device output, the Kalman filter calculates the observation noise corrected by an error correction signal according to the relative relationship between the position of the forest moving object and the position of the satellite. Since the output of the inertial reference device is corrected by the error vector calculated based on this, it is possible to accurately correct the error in the GPS receiver output that changes from moment to moment depending on the relative positional relationship between the aircraft and the satellite. Therefore, the accuracy of the position and velocity measuring device can be increased and it can be kept stable at all times.

【図面の簡単な説明】[Brief explanation of the drawing]

第1図は本発明の一実施例の説明図。 第2図は上記実施例に用いられる慣性基準装置の説明図
、 第3図は上記実施例に用いられるGPS受信機による測
位の説明図、 第4図は上記実施例における誤差修正計算部の説明図、 第5図はカルマン・フィルタでの計算の説明図、第6図
は従来の位置速度測定装置の説明図である。 図面中、 1は慣性基準装置、 1aは慣性基準装置に設けられた補正部、2はGPS受
信機、 2aはGPS受信機に設けられた誤差修正部、3はカル
マンフィルタ をそれぞれ示す。 代理人 弁理士 坂 間  暁 外2名第1図 11)、1(−):観測更祈泊の訣矛共分散行列lr;
)n(+>:観、測更tr夜の捩基共分敢行列IKn 
 :カルマンゲイン IFn:訣基モデルの状態遷移行列 Q:W!、モデルのシステム雑音 jR:観測錐肯 jH:観、測行列 足 ;単位行列 Jon(−):観測更♀片前の談基推定値父n(十):
観測更新後の誤差推定値 Zn ;観瀝り1皇〔 たた゛し、帰字几1コn番目の値な表わす。 第5図 躍?。 ! ズ諸(4)
FIG. 1 is an explanatory diagram of an embodiment of the present invention. Fig. 2 is an explanatory diagram of the inertial reference device used in the above embodiment, Fig. 3 is an explanatory diagram of positioning by the GPS receiver used in the above embodiment, and Fig. 4 is an explanation of the error correction calculation section in the above embodiment. FIG. 5 is an explanatory diagram of calculation using a Kalman filter, and FIG. 6 is an explanatory diagram of a conventional position and velocity measuring device. In the drawings, 1 is an inertial reference device, 1a is a correction unit provided in the inertial reference device, 2 is a GPS receiver, 2a is an error correction unit provided in the GPS receiver, and 3 is a Kalman filter. Agent: Patent attorney Akira Sakama and two others (Figure 1 11), 1 (-): Observation change covariance matrix lr;
) n (+>: Observation, measurement tr night rotation matrix IKn
:Kalman gain IFn: State transition matrix of base model Q:W! , system noise of the model jR: observation cone jH: observation, measurement matrix foot; unit matrix Jon(-): base estimate value before observation change n(10):
Estimated error value Zn after observation update; Expressed as the nth value of the first observation. Figure 5 dance? . ! (4)

Claims (1)

【特許請求の範囲】[Claims]  移動体の位置と速度の信号を出力する慣性基準装置、
衛星から送信される電波を捕捉し移動体の位置と速度の
信号を出力する全地球測位システム受信機、上記慣性基
準装置と全地球測位システム受信機との出力を受けこの
両出力の差である観測ベクトルに基づいて慣性基準装置
の出力を補正する誤差ベクトルを出力するカルマンフィ
ルタ、及び全地球測位システム受信機で検知された移動
体の位置と衛星の位置との相対的位置関係に応じた観測
雑音の誤差修正出力をカルマンフィルタに出力する手段
を有することを特徴とする移動体の位置速度測定装置。
an inertial reference device that outputs signals of the position and velocity of a moving object;
A global positioning system receiver that captures radio waves transmitted from satellites and outputs signals indicating the position and speed of a moving object, which receives the outputs of the above-mentioned inertial reference device and the global positioning system receiver and calculates the difference between the two outputs. A Kalman filter that outputs an error vector that corrects the output of the inertial reference device based on the observation vector, and observation noise that corresponds to the relative positional relationship between the position of the moving object and the position of the satellite detected by the Global Positioning System receiver. 1. An apparatus for measuring the position and speed of a moving body, comprising means for outputting an error correction output of the above to a Kalman filter.
JP13827587A 1987-06-03 1987-06-03 Positional speed measuring apparatus of moving object Pending JPS63302317A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP13827587A JPS63302317A (en) 1987-06-03 1987-06-03 Positional speed measuring apparatus of moving object

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP13827587A JPS63302317A (en) 1987-06-03 1987-06-03 Positional speed measuring apparatus of moving object

Publications (1)

Publication Number Publication Date
JPS63302317A true JPS63302317A (en) 1988-12-09

Family

ID=15218106

Family Applications (1)

Application Number Title Priority Date Filing Date
JP13827587A Pending JPS63302317A (en) 1987-06-03 1987-06-03 Positional speed measuring apparatus of moving object

Country Status (1)

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JP (1) JPS63302317A (en)

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2680886A1 (en) * 1991-08-30 1993-03-05 Realisa Electroniques Et Process for determining the situation of the end member of a robot and arrangement for the implementation of the process
WO1997008514A1 (en) * 1995-08-28 1997-03-06 Data Tec Co., Ltd. Movement detector
WO1998018016A1 (en) * 1996-10-23 1998-04-30 Honeywell Inc. Gps/irs global position determination method and apparatus with integrity loss provisions
US6081230A (en) * 1994-11-29 2000-06-27 Xanavi Informatics Corporation Navigation system furnished with means for estimating error of mounted sensor
WO2007148546A1 (en) * 2006-06-21 2007-12-27 Toyota Jidosha Kabushiki Kaisha Positioning device
JP2012193965A (en) * 2011-03-15 2012-10-11 Mitsubishi Electric Corp Position estimating device, and position estimating method and position estimating position program for position estimating device
WO2020021867A1 (en) 2018-07-24 2020-01-30 日本航空電子工業株式会社 Geoid measurement method, geoid measurement apparatus, geoid estimation device, and geoid calculation data collection device

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2680886A1 (en) * 1991-08-30 1993-03-05 Realisa Electroniques Et Process for determining the situation of the end member of a robot and arrangement for the implementation of the process
US6081230A (en) * 1994-11-29 2000-06-27 Xanavi Informatics Corporation Navigation system furnished with means for estimating error of mounted sensor
WO1997008514A1 (en) * 1995-08-28 1997-03-06 Data Tec Co., Ltd. Movement detector
US5828987A (en) * 1995-08-28 1998-10-27 Data Tec Co., Ltd. Movement detecting device
WO1998018016A1 (en) * 1996-10-23 1998-04-30 Honeywell Inc. Gps/irs global position determination method and apparatus with integrity loss provisions
JP2008002906A (en) * 2006-06-21 2008-01-10 Toyota Motor Corp Positioning device
WO2007148546A1 (en) * 2006-06-21 2007-12-27 Toyota Jidosha Kabushiki Kaisha Positioning device
JP4600357B2 (en) * 2006-06-21 2010-12-15 トヨタ自動車株式会社 Positioning device
US8725412B2 (en) 2006-06-21 2014-05-13 Toyota Jidosha Kabushiki Kaisha Positioning device
JP2012193965A (en) * 2011-03-15 2012-10-11 Mitsubishi Electric Corp Position estimating device, and position estimating method and position estimating position program for position estimating device
WO2020021867A1 (en) 2018-07-24 2020-01-30 日本航空電子工業株式会社 Geoid measurement method, geoid measurement apparatus, geoid estimation device, and geoid calculation data collection device
US11378397B2 (en) 2018-07-24 2022-07-05 Japan Aviation Electronics Industry, Limited Geoid measurement method, geoid measurement apparatus, geoid estimation device, and geoid calculation data collection device
EP4033204A1 (en) 2018-07-24 2022-07-27 Japan Aviation Electronics Industry, Limited Geoid estimation device, and geoid calculation data collection device
US11585657B2 (en) 2018-07-24 2023-02-21 Japan Aviation Electronics Industry, Limited Geoid measurement method, geoid measurement apparatus, geoid estimation device, and geoid calculation data collection device

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